OP, I think you need to carefully separate out "Getting exercise/moving about" versus "Sport" versus "Social participation" in your mind here. Because they are three quite different things.
It's completely reasonable to require that he does physical exercise in some shape or form--that's on par with going to bed at a proper time, limiting screen time, eating properly etc.
Sport, on the other hand? Some people like sport, some hate every sport, some like certain things but not others. No parent has a right to make children play sports, IMO. And frankly, a lot of sports don't actually provide very much exercise, especially to those who aren't very good at them. Kids who hate cricket and are forced to play anyway, will just stand uselessly about. It's a waste of time.
Agree with others, you need to get out for family walks and bike rides. If he moans, make it clear to him that he is required to take part anyway, and that "it's either this, or you need to propose another physical activity that you WOULD like to do, I'm afraid". As a parent, it's fine to require exercise.
I know it's tough to deal with a kid who doesn't want to move and whines about it.... I don't have any magical solutions here, though, other than to point out that it's just part of the job of being a parent! (I have a daughter who did not want to swim or ride a bike for the longest time, both non negotiable as far as I am concerned. It was exhausting, but she finally got over it and now does both).
You really really need to drop this focus on team sports and especially football. Team sports are torture on those who aren't good at sport. And football is the absolute worst sport to try and get an unsporty older child into--it is so popular that some kids will have been coached and trained since they were three years old!
If you do want him to do an activity of some kind, it will most likely need to be something solitary, non-competitive or both. Geocaching, climbing...? Forget traditional ideas about sportiness and think in terms of "moving about."
You mentioned "Every time he is not picked"--if the school is allowing kids to pick teams, they need to be approached about this and told that this is not OK. It's bullying, it's lazy PE practice and it makes a lot of children hate the very idea of exercise.
Re the social participation thingthe fact that most of the boys in his class are into football? That's hard, but if he is useless at football and doesn't want to do it, then forcing him to make a fool of himself on a team is not exactly going to improve his standing. Perhaps there are other out of school activities that he might enjoy doing instead. If the school is so hyper focused on football, it might not be the best place for himwould a move be feasible? That said, things will most likely get better at secondary. As a PP said, some boys will continue to be into football, some will not, and in the bigger social environment of the average secondary there is a lot more room for different kids to find their own "kind."